Global Parameterization of Multiple Point-Defect Dynamics Models in Silicon

Authors: Erich Dornberger, Hartmut Bracht, Robert Hoelzl, Talid Sinno, Thomas A. Frewen, Wilfried von Ammon
Publication Date: September 15, 2003
Journal: Journal of the Electrochemical Society

Citation: T. Frewen, T. Sinno, E. Dornberger, R. Hoelzl, W. von Ammon, and H. Bracht, Parameterization of Transient Defect Dynamics Models in Czochralski Silicon Crystal Growth, Journal of the Electrochemical Society, 150 (2003) G673-G682.

Abstract: The task of determining globally robust estimates for the thermophysical properties of intrinsic point defects in crystalline silicon remains challenging. Previous attempts at point-defect model regression have focused on the use of a single type of experimental data but as of yet no single parameter set has produced predictive models for a variety of point-defect related phenomena. A stochastic optimization technique known as simulated annealing is used to perform simultaneous regression of multiple models. Specifically, zinc diffusion in Si wafers and the dynamics of the so-called interstitial-vacancy boundary during Czochralski crystal growth are used to systematically probe point-defect properties. A fully transient model for point-defect dynamics during crystal growth is presentedwhich employs a sophisticated adaptive mesh refinement algorithm to minimize the computational expense associated with each optimization. The resulting framework leads to a quantitatively coherent picture for both experimental systems, which are modeled with a single set of point-defect thermophysical properties. The results are shown to be entirely consistent with other recent model-fitting estimates and indicate that as the number of experiments considered simultaneously within this framework increases it shouldbe possible to systematically specify these properties to higher precision.